We note that the aforementioned channel estimation methods mainly focus on the pilot design, reflection coefficients optimization and specific estimation algorithms, which are crucial and challenging tasks in IRS-assisted wireless systems [1]}, [2]}, [3]}, [4]}. Nevertheless, there are still some points that can be exploited to further improve the efficiency of the IRS. For example, existing channel estimation methods generally adopt the constant-envelope pilot signals for each user/antenna without considering the pilot power allocation during the channel estimation phase. In [5]}, we have discussed the pilot power allocation in the single-IRS assisted communication systems and performed the power allocation between the pilots used for estimating the direct link and reflection links. Nonetheless, there exist some limits to the rate performance improvement [5]}. On one hand, the user gains the performance benefits only in the vicinity of the IRS due to the high path loss, which is the area where the path loss of the reflection channels is significantly severe than that of the direct channel. On the other hand, the IRS is generally equipped with a large number of reflecting elements to compensate for the high path loss. Due to the asymmetry between the direct link and reflection links, the displayed performance improvement in [5]} is limited, e.g., only effective for a small/moderate number of reflecting elements at the IRS. Furthermore, we note that much of the prior works focus on the communication systems assisted by a single IRS, few of them focus on the design of multiple-IRS assisted communication systems [8]}, [9]}.
